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Effective Areas and Liquid Film Mass Transfer Coefficients in Packed Columns Roberto Echarte, Horaclo CampaEa, and Esteban A. Brlgnole' Planta Piloto de Ingenler??QGmica UNS-CONICET,
C.C.717, 8000 Bahh Blanca, Argentina
The effect of viscosity on liquid-side mass transfer coefficients in packed columns is discussed, and experimental data obtained in a 0.4 m i.d. packed column are reported on the desorption of carbon dioxide from water and water-glycerol solutions for 0.058-m ceramic Raschig rings. Effective areas for physical absorption are obtained, in the same packed column, by means of a new technique based on the process of cooling of water. Experimental values of H L were obtained over a wMe r a n p of Reynolds ( R e ) , Schmidt (Sc), and Gallleo (Ga)numbers. These data are well correlated with {HLGa '''ISc *) vs. Re over the following ranges: 300 < Sc < 10 000,6.0 X lo7 < Ga < 230 X lo7, and 30 < Re < 800. This correlation is based on the penetrationtheory combined with the fluid mechanics of a laminar failing film, and the Re number to be used in the Correlation is computed by use of the effective area for physical absorption. The present results are also helpful in the interpretationof the effect of gravity and surface tension on liquid-side mass transfer in packed columns.
Introduction The rate of mass transfer between gas and liquid in a packed column depends upon the concentration of the transferring species in both phases, liquid and gas physicochemical properties and flow rates, and on size, shape, and material of the packing. Since the early work of Sherwood and Holloway (1940) a wealth of data has been collected on mass transfer in packed columns. Excellent reviews of this subject have been done by Sherwood et al. (1975) and by Norman (1962). In spite of the large amount of information available on packed column performance, there are still some areas where the design or simulation of packed columns is subject to uncertainties. One of these is the effect of the physical properties of the liquid upon the mass transfer coefficient. Among the physical properties, the surface tension, solute diffusivity, and liquid density and viscosity play a major role in determining the rate of mass transfer in the liquid film. The volumetric mass transfer coefficient is the product of the effective area per unit volume and the individual mass transfer coefficient. From the point of view of the physical properties, the effective area will depend mainly on the surface tension, liquid density, and packing material. On the other hand, the liquid side mass transfer coefficient will depend mainly upon solute diffusivity and liquid viscosity. The effect of solute diffusivity is well established; however, this is not the case with viscosity. In Table I are listed some of the best known correlations of liquid side mass transfer data in packed columns,together with the relevant power dependence of HL on viscosity. The exponent of viscosity varies from a negative value, 4.05, to +1.0. The lack of agreement on the exponent of viscosity, among the correlations listed in Table I, is due to the fact that the correlations are based almost entirely on experimental data obtained for aqueous systems or organic liquids of similar viscosity. This points to the need of mass transfer data in packed columns over a wider range of liquid viscosities. Hikita and Ono (1959), using a single piece of packing, and Norman and Sammak (1963a,b) and Vitovec (1968), working with disk columns, have reported experiments on the effect of viscosity on liquid-side mass transfer coefficients. The results of Hikita and Ono (1959) and Norman and Sammak are valuable to study the effect of viscosity, but their data are not directly applicable to packed col0796-4305/8411123-0349$01.50/0
Table I. Dependence of HT.on Viscosity: H I . = q p m correlation
m
Sherwood and Holloway (1940) Van Krevelen e t al. ( 1 9 4 7 ) Shulman e t al. (1955b) Onda e t al. (1968) Yoshida and Koyanagi ( 1 9 6 2 ) King ( 1 9 6 0 ) Semmelbauer ( 1 9 6 7 ) this work
0.15-0.28 1.00 -0.05 0.93 0.333 0.43
0.88 0.46
umns. Mangers and Ponter (1980),working with a column 10 cm in diameter and packed with 1-cm glass Raschig rings, obtained valuable data on the effect of viscosity on the liquid film resistance to mass transfer, but their results are difficult to extrapolate to larger packing sizes. With regard to the experimental data needed in packed columns, it should be pointed out that it is valuable to study liquids with different viscosities but with only minor changes in surface tension. Besides, it is necessary to measure in the same columns effective areas for the packings under study at different gas and liquid flow rates. This information will aid the understanding of the effect of viscosity and will shed some light on the influence of body force and surface tension on liquid-side mass transfer coefficients and effective areas in gas-liquid countercurrent packed columns. Liquid-Phase Mass Transfer in Packed Columns Under the conditions usually found in practice, laminar flow prevails in the liquid film, and a penetration type model is valid for the diffusion of solute into the liquid phase. On this basis, several authors have proposed equations of the following form
Vivian and Peaceman (1956) derived this equation for wetted wall columns on the basis of penetration theory combined with the fluid mechanics of a laminar falling film. Davidson (1959), on the same basis, extended this equation to packed columns. He assumed several models for the orientation and length of the packing surfaces and obtained different equations for f , ( R e ) , all of the form fi(Re) = CiRe213
0 1984 American Chemical Society
(3)
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where Ciis a constant for each proposed model. Yoshida and Koyanagi (1962), in packed columns, Norman and Sammak (1963a) and Hikita and Ono (1959), in disk columns, have obtained expressions for f i ( R e ) f i ( R e )= C,Reni (3) in which the exponent 2 / 3 on the Reynolds number has been replaced by an empirically determined exponent. It should be stressed here that the Reynolds number to be used in these equations is the one that governs the flow of liquid films: Re = (4r/p) or (4Llap); where a is the packing area associated with an active liquid flow: in other words, the effective area for physical absorption. As has been shown by Davidson (1959), the exponent 2/3 on the Reynolds number is obtained theoretically from: (1)the penetration theory, (2) the Nusselt equation for predicting the velocity in a falling film, and (3) the assumption of complex mixing in the liquid film at given distances in the packing. It is reasonable to assume that in a packed column the active portion of the liquid film will be associated, as an average, with a given path length between mixings, but it is unrealistic to think of this length as independent of the liquid flow rate; moreover, it should depend upon the true liquid Reynolds number (4Llak). Therefore it is convenient to relax the assumption of constant length. Instead, the dimensionless average path length is taken to be a function of the Reynolds number. From penetration theory the mass transfer coefficient is given by (4) where us is obtained from the Nusselt equation for the superficial liquid velocity in a falling film
and from the assumption that the average path length 1 is a function of the Reynolds number 1 / d = qiRe-mi (6) where qiand miare constants for each packing. Equation 4 can be written in terms of HL as follows (7)
If us and 1 of eq 7 are substituted using eq 5 and 6, the denominator becomes
(84 Grouping all the constants in C! and regrouping the variables as to obtain the Sc and Ga numbers
4p [ 4Dus ]'Iz -
Substituting this result into the eq 7 and rearranging
Equation 9 reduces to eq 2 for m = 0 and to eq 3 for m greater than zero. In previous works the experimental values of the exponent on the Reynolds number have been found smaller than the theoretical 2 / 3 . Vivian and King (1964) ascribed this effect to the decreasing of the average length between surface renewals with increasing liquidphase Reynolds number. Norman and Sammak (1963a,b), however, considered that the degree of mixing between packing elements was not perfect and depended upon the Reynolds number. The net effect is similar, since imperfect mixing will mean a greater path length for a complete surface renewal. The exponent on Schmidt number in eq 9 results from penetration theory. This value has been confirmed by Vivian and King (1964) in a packed column over a wide range of gas and liquid rates. Shulman and Melish (1967) obtained experimental evidence on the laminar nature of the liquid flow in a packing; therefore, the exponent ' / 6 on the Galileo number is justified. It should be stressed that in using eq 1 , 2 , 3 , or 9 the value of the effective area must be independently known. Mangers and Ponter (1980) found that their data on liquid-side mass transfer coefficients for 1.0-cm glass Raschig rings, obtained from absorption of C 0 2 in water glycerol solution experiments, were not adequately correlated by using a rearranged version of Norman and Sammak (1963a) correlation for a disk column. But the lack of experimental data on effective areas for the packing under study precluded them from making a critical test of this equation using their own data. Besides, the experimental results of Mangers and Ponter depicted a change of liquid flow regime at the higher viscosities and liquid flow rates, where the laminar falling film flow no longer prevails and there is a transition to a different flow regime where, as it is suggested by these authors, the liquid becomes the continuous phase and gas bubble flow results. Under these conditions the assumptions that lead to eq 1 or eq 9 are no longer valid. This flow regime is characteristic of the loading and flooding phenomenon in packed columns at low gas rates. The occurrence of this change in flow regime is favored by the properties of a small packing, like the one used by Mangers and Ponter, of having a small porosity and high liquid holdup. Besides, Shulman et al. (1955~)reported a large increase in liquid holdup at viscosities greater than 10 cP. During the present work, the experimental conditions were below loading, and the interaction of the gas flow upon the liquid side mass transfer coefficients (kL)could be neglected. The main purpose of this investigation is the study of the effect of liquid physical properties upon kL. In the same packed columns effective areas are measured at the gas and liquid rates of interest. The effect of physical properties on kL was studied by using processes entirely controlled by the liquid side resistance: the desorption of C 0 2 from water glycerol solutions. With this system it was possible to vary the Schmidt and Galileo numbers over ranges not normally employed in previous studies. Therefore, the present results are useful to test the soundness of eq 3 or 9 to interprete liquid-film mass transfer in packed columns. Experimental Apparatus The runs for the desorption of C 0 2 from water were carried out in a packed column similar to the one used by Vivian and King (1964). The packed column diameter was
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 351
0.40 m. Some modifications were introduced to the original design to allow for performing different kinds of experiments and to reduce end effects. The liquid distributor consisted of a cylindrical drum, 0.15 m high and 0.36 m in diameter with 90 holes of 0.003 m. It discharged the liquid directly over the packing. Twenty-four tubes of 0.04 m i.d. were fitted between the top and bottom plates of the distributor to allow for the passage of air. Two packings with applications in industrial practice were used in this investigation: 0.025-m and 0.058-m ceramic Raschig rings. In the experiment of C02desorption from water-glycerol solutions the liquid was first circulated through an additional packed column, without countercurrent flow of air. This was required to break the emulsion of small bubbles of gas trapped in the viscous liquid solution. The water-cooling runs were performed using the same apparatus. Heat was supplied to the liquid by introducing steam directly into the recirculating tank. The packed column and all the inlet and outlet lines were thermally insulated. Experimental Procedure. Desorption of C 0 2 from Water-Glycerol Solutions. Before each series of runs the tower was operated at a high liquid rate in order to establish the liquid holdup in the column. The concentration of disolved gas was determined following the procedure recommended by Sherwood and Holloway (1940). Duplicated samples were taken from the bottom and the top of the column for each run. The difference in the inlet and outlet temperatures of the air streams was always kept below 1 "C. Glycerol 99.5% was used. The neutrality of the glycerol was checked following standard procedures. Before and after each run liquid samples were taken to measure the density, viscosity, and concentration of the water-glycerol solutions. The viscosities were measured with calibrated Cannon Fenske viscosimeters and the values were corrected to the mean temperatures of the liquid in the tower; this correction was always less than 1.5%. The concentration of glycerol in water was determined from the density of the solution. The concentration-viscosity data obtained in this work were found to be in excellent agreement with the data of Sheely (1932). The solubility data of C 0 2 in water-glycerol solutions were obtained from Buzek and Jaroszynski (1973). Cooling of Water. The wet and dry bulb temperature method was used to determine air humidity. This method was checked several times against the gravimetric method and good agreement was found. The thermometers were mounted following the recommendations of Lynch and Wilke (1955). Liquid temperatures were measured at the water inlet and at the bottom liquid pool level with thermistor sensors calibrated to 0.1 O C . The inlet and outlet gas temperatures were measured immediately before the air distributor. In each run the following data were recorded: gas and liquid rates, inlet and outlet wet and dry bulb temperatures, inlet and pool liquid temperatures, air temperature before and after the packed section, and atmospheric and operating pressure.
Mass Transfer Results The effect of liquid rate upon HL was investigated for the 0.058-m ceramic Raschig rings. The liquid rate was varied between 9000 kg/m2 h and 50000 kg/m2 h. The gas rate was kept constant at 1000 kg/m2 h to avoid the loading regime. Experiments were run at two different packed heights to check if there were any noticeable end effects in the desorption of C02 from water studies; however, reproducible results of HL were obtained at 0.33 m and 0.90 m.
3.0 I
01
4
6
0
lo6
2
d
6
8 10'
L [ kg/m2 h l
Figure 1. Effect of viscosity upon HL.Packing: 0.058-m ceramic Raschig rings; G = 1000 kg/m2 h; glycerol concentration (in weight): (A)0%; (A)24.9%; (0) 39.2%; ( 0 )50.33%; temperature, 25 O C .
I 2r103
C
6
8
lo4
2
,
wo4
L [kg/m'hrl
Figure 2. Cooling of water. Uncorrected HGdata at two different packed heights; G = 2000 kg/m2 h; packing size: (A,0) 0.025 m; (A, 0 ) 0.058 m; packed height: (A)0.30 m; (A)0.36 m; ( 0 )0.52 m; (0) 0.57 m; (-) corrected HG data.
The effect of liquid viscosity and solute diffusivity upon
HL was investigated for the 0.058-m ceramic Raschig rings by studying the desorption of C02 from water-glycerol solutions in the same packed column using a packed height of 0.9 m. The viscosity range covered was from 0.87 to 6.1 cP. The effects of viscosity and liquid rate upon HLare shown in Figure 1. The water cooling experiments were carried out to obtain the height of the gas side transfer unit, HG. Even though the end effects have been found negligible for the liquid-side controlled experiments, this no longer holds true for a gas-side mass transfer controlled process. Therefore, HG values were measured at two different packed heights to correct the HG values for end effects. This correction amounted to less than 10% of the HG values obtained at the higher packed bed. For illustration, uncorrected HGvalues obtained at two different packed heights are shown in Figure 2 together with the corrected values for 0.025-m and 0.058-m ceramic Raschig rings. Effective Areas for Physical Absorption. The effective areas were measured following the method proposed by Weisman and Bonilla (1950). In this method the variation of the HGvalue, obtained from physical absorption of a highly soluble gas, relative to the HG value which corresponds, at the same gas rate, to that produced by a column packed with a thoroughly wetted porous packing, is ascribed to the differences in the effective area in each case. The HGvalues for the ceramic Raschig rings were obtained using the Taecker and Hougen (1949) correlation. Yoshida and Koyanagi (1962) measured effective areas following this procedure. They used the absorption of methanol in water for this purpose. Shulman et al. (1955a) measured effective areas using their own correlation for
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Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
HGbased on the sublimation of naphthalene Raschig rings, and Fellinger’s data (1941) of ammonia absorption in water. In the present work HG values are obtained from water cooling in a packed column with countercurrent flow of air. The water cooling is a source of gas-side mass transfer coefficients, comparable to methanol or ammonia absorption in water. In both cases the semistagnant, slowly moving parts of the liquid film surface are almost noneffective in the physical absorption process. The water-cooling experiments have not been used previously to obtain effective interfacial area for physical absorption. This technique was preferred in this work, rather than ammonia or methanol absorption in water, because the latter procedures may induce a change in the wettability of the packing. Surface tension disturbances in a falling f i i that occur during the absorption of highly soluble gases lead to instability of the film which breaks up into rivulets and drops. These phenomena have generally been explained by the Marangoni effect (Sternling and Scriven, 1959; Zuiderweg and Harmens, 1958). Ford and Missen (1968) have provided the following stability criteria based upon the Marangoni effect: if do/db I O , film is stable (10) and if da/db
> 0, film is unstable
(11)
the latter being a necessary but not a sufficient condition. Physically eq 10 means that if “thin regions of the film are of higher surface tension, the film is stabilized by contraction of these regions and spreading of the thick regions so as to create a more uniform thickness”. On the other hand, the situation is reverse for the physical situation pictured by eq 11. During the water cooling in a packed column, the thin slow moving parts of the liquid film tend to be colder and hence of higher surface tension. Therefore, eq 10 is fulfilled for this system and the liquid film is stable. The absorption of ammonia or methanol in water is potentially unstable because da/db is greater than zero. Bond and Donald (1957) have shown experimentally that the minimum wetting rate in a wetted wall column increased tenfold relative to the case without ammonia absorption as the concentration of ammonia in the inlet gas increased from 5% to 50% in volume. Another good feature of using the water cooling as a source of HG values is that most of the mass transfer experiments with porous wetted packing have been carried out with the air-water system. Therefore, no correction for differences in diffusivities is neces_saryin comparing the HG values of water cooling with HG. Following the method proposed by Weisman and Bonilla (1950), the relationship between effective and total area is -a= - RG UT
HG
This equation has been modified in the present work to take into account the effect on Ho,of the change in packed bed porosity of an irrigated packed column, due to the liquid holdup. Gupta and Thodos (1962) found that HG is proportional to the bed porosity at a given gas flow rate. Introducing this porosity correction factor in eq 1 2
where z is the porosity of the nonirrigated packed bed and
i
I
G :2000
kg/m2h
Figure 3. Effective areas for ceramic Raschig rings c is the porosity of the bed at the operating gas and liquid flow rates in the column. The corrected HG values from Figure 2 together with c values, obtained by substracting from 7 the total liquid hold up of the packing, were used in eq 13 to obtain the effective areas depicted in Figure 3 for the two packing materials. The effective areas for 0.0254-m ceramic Raschig rings can be compared with the values reported by Shulman et al. (195513) for the same packing. It is found that the present values are on the average 20% higher. However, this discrepancy is mainly due to the different HG correlation used in each case. Correlation of Liquid Side Mass Transfer Data The effect of liquid viscosity upon HL is shown in Figure 1 for the 0.058-m ceramic Raschig rings. These are raw data to test the validity of eq 3. The dimensionless variables that appear in eq 9 were varied over the following ranges 6 C H L / d C 36
300
C
Sc < 10000
6.0 x lo7 C Ga C 230 x lo7 30 C Re C 800 The Reynolds number was varied through changes in viscosity and liquid rate. To compute its value, the effective areas at each operating condition were obtained from Figure 3. It was assumed that the effective areas were the same for the water-glycerol solutions as for water. This assumption is supported by the fact that the surface tension of the solution changes 4% over the entire range of glycerol concentration. Besides, the experimental data of Onda et al. (1967) show that the change of wetted area with glycerol concentration in water is very low. However, Mangers and Ponter (1980),have claimed that the wettability of glass packings by aqueous glycerol mixtures increases with increasing glycerol concentration. This effect could be more significant for the small packing size used by these authors: 0.01-m glass Raschig rings. For this size of packing only a small fraction (10-15%) of the geometric area is effective for mass transfer in water-irrigated columns. In the case of the packing used in the present work, due to its large size, the effective area is already from 60 to 90% of the total surface of the packing; therefore the relative increase of the effective area due to a better wettability of the packing will be less important. In any case, due to the lack of information of effective areas for aqueous glycerol systems, the effective areas obtained for water will be used to compute the Reynolds number throughout this work.
Ind. Eng. Chem. Process Des.
Dev., Vol. 23,
No. 2, 1984 353
I
2.0,
I
1
0
2
:
L
:
6
Viscosity
(cP)
Figure 4. Diffusivities of carbon, dioxide in waterglycerol solutions at 25.0 "C: (A)Astarita (1964); (0)Onda et al. (1960); (X) Calderbank (1959); ( 0 )Brignole and Echarte (1981). 1001
I
I
I
10
1000
100
NR~
Figure 5. Correlation of liquid side mass transfer data for 0.058-m ceramic Raschig rings.
The experimental values of carbon dioxide diffusivity in water glycerol solutions reported by several authors show some disagreement (see Figure 4); therefore, a careful experimental study was carried out (Brignole and Echarte, 1981) to obtain reliable diffusivity values, for this system, for the computation of the Schmidt number. Values of the group (HL/d) Ga1f6/Sc'/2for each experimental run are plotted vs. the Reynolds number in a log-log graph in Figure 5 for the 0.058-m ceramic Raschig ring. The data are correlated by using eq 3 with n = 0.375 and C' = 1.552 with a correlation coefficient of 98%. In Figure 6 are plotted the data of Holloway (1939) for Raschig rings of several sizes: 0.025, 0.038, and 0.051 m, using the desorption of O2from water. The effective areas were estimated with the correlation of Mada et al. (1964) ad = 0.34
We2I3 -
(14) Fr1J2 This correlation is mainly based on the experimental values of effective areas obtained by Shulman et al. (1955b) and Yoshida and Koyanagi (1962). It was chosen to correlate the data of Holloway because it depided an effect of liquid flow rate on the effective area similar to the one found in the present work and because it was valid in the desired range of packing sizes. In spite of the fact that the Galileo number is varied only through changes in packing diameter, the data are fitted reasonably well by eq 3 using n = 0.367 and C' = 1.580 with a correlation coefficient of 96.7%. From these values, the net effect of viscosity variation on HL can be obtained. The power dependence of HL on viscosity is found to be 0.46. I t was attempted to correlate the present data
1O1
lo,
NRe
Figure 6. Correlation of liquid-side mass transfer data for ceramic Raschig rings. Packing size and source: (0)0.058 m, this work (A) 0.0254 m; (0) 0.038 m;(a)0.051 m, Holloway (1939).
without the Galileo number, as is done in the Sherwood and Holloway correlation. When the present data are plotted in that way, it is not possible to obtain a general correlation, and different lines are obtained for each glycerol concentration. The correlation proposed by Onda and co-workers (1959, 1968) was also tested with the present data and no satisfactory fit was obtained. The failure of the Onda correlation for dealing with large differences in viscosity can also be seen from their own data on C 0 2 absorption in ethanol ( u = 1.5 cSt) and carbon tetrachloride ( u = 0.6 cSt). The carbon tetrachloride data lie on a line 35% below the ethanol data.
Effect of Gravity and Surface Tension Vivian et al. (1965) obtained the only experimental data available on the effects of gravity upon HL. They found that the effect of gravity was considerably greater than the ' I 6power shown by eq 1. The effect of gravity upon the effective area was not measured. The observed effect of the gravity force upon HL is likely to be the result of a variation, not only in the values of the Galileo number, but also in the Reynolds number. Even though an exact formulation is not attempted here, the spreading of a liquid over a partially wetted packing surface will depend mainly upon a balance between inertia forces, body forces (gravity) and gb-liquid-solid surface forces with the viscous forces playing a minor role. The influence of the inertia forces is readily seen from the increase of effective area with liquid rate. It is likely that the body forces play a similar role. According to Vivian et al. (1965), it is quite probable that the experimentally found effect of gravity upon HL is partly due to an increase of effective area with increasing body forces. A correlation of effective areas as a function of Froude and Weber numbers has been proposed by Mada et al. (1964). This correlation is based on experimental data on aqueous and organic liquid systems flowing over beds of Raschig rings and Berl saddles. This correlation depicts a variation of the effective area with the square root of gravity. The correlation of Mada et al. is applicable only to wetting systems. Onda et al. (1967) and Puranik and VogelpohI (1974) have developed correlations that use the concept of critical surface tension of the packing material. This parameter enables them to take into account the differences of wettability of the solid surface. All correlations agree reasonably well with the quantitative predictions of the effect of liquid rate, the most studied phenomenon, but differ with respect to the effect of gravity and the physical properties of the liquid film. This discrepancy points to the need for more experimental data on the effective areas for liquids of extreme values of density and surface tension. In that sense, the data of
354
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
Mackey and Warner (1973) on evaporation of mercury in irrigated packed columns are valuable, as are the effective areas obtained from them. The data of C 0 2 absorption in methanol are useful to study the effects of liquid surface tension on mass transfer. This system has a surface tension three times smaller than water. Yoshida and Koyanagi (1958) obtained data on absorption of COz in methanol and water in a packed column and also reported values of effective areas for both systems. The HL values for water wee considerably greater than those for methanol; at a given liquid rate the ratio between the HL values for both systems varied between 1.8 and 2.2. The value for this ratio predicted with the help of eq 3, using the effective areas reported by these authors, is 2.29. In using eq 3 the diffusivity of COz in methanol was taken from the data of Gogineni (1965),who reported a value D = 6.4 X cmz/s at 25 "C and corrected it to 15 "C with the help of the Stokes-Einstein relation. Hikita et al. (1960)reported experimental values for water and methanol which show the ratio between HL for the two systems to be 2.5. These authors do not give data on the effective areas for the systems studied. If the effective areas are estimated with the correlation of Mada et al. (1964), the ratio of HL obtained with eq 3 is 2.58. In both cases the agreement between the observed and predicted values is quite good. It should be pointed out that, as the surface tension does not appear explicity in eq 3 in the foregoing prediction, the surface tension has been considered only with reference to the value of the effective areas. Therefore, in the absence of interfacial instabilities or surface active agents, it is only through the effective area that HL varies with the liquid surface tension.
Conclusions Liquid-side mass transfer data were obtained by using water-glycerol solutions in a packed column. The operating conditions studied covered a wide range of Reynolds, Schmidt, and Galileo numbers. The experimental values of HLare well correlated with the help of eq 3, which is based on penetration theory combined with the fluid mechanics of a laminar falling film. The results obtained support the use of the effective area to compute the liquid-side Reynolds number of an irrigated packed bed. The cooling of water by a countercurrent flow of air is proposed for the determination of effective areas for physical absorption in packed columns. The main advantage of the water cooling process over that of absorption of a high soluble gas is that in the former the liquid film is always stable under interfacial surface tension gradients. The experimental data of effective areas obtained from water-cooling experiments are in good agreement with previous results. Nomenclature a = effective interfacial area per unit volume of packed bed aT = total surface area per unit volume of packed bed b = liquid film thickness d = nominal dimension of the packing D = diffusivity G = gas flow rate per unit cross-sectional area of column g = local gravity HG= gas-side height of a transfer unit HG= gas-side height of a transfer unit for a completely wetted packed bed
HL = liquid-side height of a transfer unit
kL = liquid-side mass transfer coefficient L = liquid flow rate per unit cross-sectional area of column 1 = average distance between mixing points in the liquid film T = temperature u, = velocity of the surface on the liquid film Greek Letters = packing porosity at the operating gas and liquid flow rates z = porosity of non-irrigated packing p = density = dynamic viscosity u = surface tension
r = peripheral liquid flow rate
v =
kinematic viscosity
Dimensionless Numbers Fr = Froude (L2/pzgd) Ga = Galileo (p2gd3/p2) Re = Reynolds (4L/ap) We = Weber ( d L 2 / p u ) Sc = Schmidt ( p / p D )
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Received for review November 19, 1981 Revised manuscript received May 26, 1983 Accepted June 20, 1983
